Geometry · SSC CGL previous year questions

A vertical pole of height H stands on the ground. From a point P on the ground, the angle of elevation of the top of the pole is 60°. From a different point Q, located 10 meters away from point P (directly along the line extending from the base of the pole), the angle of elevation to the top of the pole is 30°. What is the height of the pole?

1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4

In △ABC and △XYZ, AB = XY, BC = YZ, and CA = ZX. By which congruence rule are the two triangles congruent?

1. A.SSS
2. B.SAS
3. C.ASA
4. D.RHS

In a cyclic quadrilateral ABCD, the angle A is 100°. What is the measure of the angle C?

1. A.70°
2. B.80°
3. C.90°
4. D.110°

If (48° + k) is an acute angle and sin(48° + k) = cos13°, what is the value of k (in °)?

1. A.23
2. B.17
3. C.37
4. D.29

If A is an acute angle and tanA + cotA = 2, find the value of 7tan⁸A – 6cot⁸A + 8sec²A.

1. A.7
2. B.16
3. C.17
4. D.6

For triangles, which of the following statement(s) are true? (a) Sum of interior angles is 180°. (b) All interior angles can’t be equal. (c) Can have at the most one obtuse angle. (d) Sum of two sides may or may not be equal to the third side.

1. A.(a) and (b)
2. B.(a), (b) and (d)
3. C.(a) and (c)
4. D.(b), (c) and (d)

In a , right angled at B if , then find .

1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4

In a triangle PQR, ∠P + ∠Q = 84°. Find the value of ∠R.

1. A.74°
2. B.96°
3. C.102°
4. D.60°

In triangle XYZ, A is a point on YZ such that XA = YA. If ∠XYA = 50° and ∠AXZ = 19°, what is the degree measure of ∠XZA?

1. A.61°
2. B.53°
3. C.49°
4. D.41°

If the altitude from two vertices of a triangle to the opposite sides are equal, then the triangle will be:

1. A.equilateral triangle
2. B.isosceles triangle
3. C.scalene triangle
4. D.obtuse angle triangle

If the lengths of two sides of an isosceles triangle are 6 cm and 12 cm, then find the length of the third side.

1. A.8 cm
2. B.12 cm
3. C.14 cm
4. D.6 cm

In a quadrilateral ABCD, AB = BC, AD = DC. ∠ABD = 68°, ∠ADB = (2y-7)°, ∠BDC = 33°, ∠DBC = (3x+2)°. Then the value of 2x+3y is:

1. A.104
2. B.108
3. C.118
4. D.144

Triangle XYZ is an isosceles triangle with sides XY = XZ. If the measure of angle Y is 80°, what is the measure of angle X?

1. A.30°
2. B.40°
3. C.50°
4. D.20°

If , then A = ________, where 3A is an acute angle.

1. A.78°
2. B.26°
3. C.29°
4. D.52°

If 3 tan A = 4 and A is an acute angle, then the value of 4sinA + 3cosA is:

1. A.1
2. B.4
3. C.5
4. D.3 cosec

Let ABC be a triangle. If the mid-points of AB, BC and AC are D, E and F, respectively, then ΔDEF is NOT congruent to _______.

1. A.ΔBDE
2. B.ΔADF
3. C.ΔECF
4. D.ΔABC

Study the given pie chart carefully and answer the question that follows. The given pie chart depicts the expenditure incurred towards different hobby classes of an institute. If the total expenditure is ₹10,70,000, then find the central angle of the sector representing ‘drawing’.

1. A.70°
2. B.68.4°
3. C.19°
4. D.90°

In ΔABC, AB = 6 cm, BC = 9 cm and AC = 12 cm. If AD is the angle bisector of ∠BAC, where D is a point on BC, then DC (in cm) is equal to:

1. A.7
2. B.3
3. C.6
4. D.9

In the following sets, which set represents the sides of a right-angled triangle?

1. A.{5, 10, 12}
2. B.{3, 4, 6}
3. C.{5, 12, 13}
4. D.{8, 15, 16}

Which of the following are the angles of a scalene triangle?

1. A.60°, 30° and 90°
2. B.110°, 35° and 35°
3. C.60°, 60° and 60°
4. D.90°, 45° and 45°

If each side of an equilateral triangle is 37√3 cm, then its altitude (in cm) is equal to:

1. A.37.5
2. B.18.5
3. C.60.5
4. D.55.5

If $\tan A=\frac{1}{\sqrt{10}}$, A is an acute angle, then the value of $\sin A+\mathrm{cosec}A$ is:

1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4

P, Q and R are the three angles of a triangle. If P − Q = 20° and Q − R = 26°, then ∠P is equal to:

1. A.82°
2. B.46°
3. C.52°
4. D.92°

WXYZ is a quadrilateral in which XQ and ZP are perpendicular to WY such that XQ = ZP. Diagonals ZX and WY intersect each other at point O. If OX = 12 cm, then find the value of ZX (in cm).

1. A.18
2. B.24
3. C.36
4. D.12 cosec cosec

If $3{\sin }^2\theta +5{\cos }^2\theta =4$ and $\theta$ is an acute angle, then the value of $\tan \theta$ is:

1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4